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Simplifying 4x3 + -9x2 + -6x = 0 Reorder the terms: -6x + -9x2 + 4x3 = 0 Solving -6x + -9x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -9x + 4x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-6 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying -6 + -9x + 4x2 = 0 Solving -6 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -2.25x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.25x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.25x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.25x + x2 = 0 + 1.5 -2.25x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.25x + x2 = 1.5 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 1.5 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 1.5 + 1.265625 Combine like terms: 1.5 + 1.265625 = 2.765625 1.265625 + -2.25x + x2 = 2.765625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (x + -1.125) equal to 1.663016837 and -1.663016837.Subproblem 1
x + -1.125 = 1.663016837 Simplifying x + -1.125 = 1.663016837 Reorder the terms: -1.125 + x = 1.663016837 Solving -1.125 + x = 1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.663016837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.663016837 + 1.125 x = 1.663016837 + 1.125 Combine like terms: 1.663016837 + 1.125 = 2.788016837 x = 2.788016837 Simplifying x = 2.788016837Subproblem 2
x + -1.125 = -1.663016837 Simplifying x + -1.125 = -1.663016837 Reorder the terms: -1.125 + x = -1.663016837 Solving -1.125 + x = -1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.663016837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.663016837 + 1.125 x = -1.663016837 + 1.125 Combine like terms: -1.663016837 + 1.125 = -0.538016837 x = -0.538016837 Simplifying x = -0.538016837Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.788016837, -0.538016837}Solution
x = {0, 2.788016837, -0.538016837}
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